Practice Test 19 - Algebra 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. Should the boundary line for the inequality $y \le -x + 4$ be solid or dashed?
2. A town's population is modeled by $P(t)=500(0.90)^t$, where $t$ is in years. What does the base $0.90$ represent in this context?
3. Why doesn't "irrational $\times$ irrational" have a single always-true result type? Choose the option that correctly supports the answer using two examples (one rational product and one irrational product).
4. An algorithm's processing time is modeled by $T(n) = 3 \cdot 4^{n/3}$ where $n$ is the input size. Which transformation reveals the processing time growth factor when input size increases by 1?
5. Derive the finite geometric series sum formula. Starting from $S_n=a+ar+ar^2+\cdots+ar^{n-1},$ which expression correctly results from multiplying by $r$ and subtracting to eliminate the middle terms (assume $r\ne 1$)?
6. Explain how $b^{m/n}=(\sqrt[n]{b})^m$ extends integer exponent properties. Which statement gives the correct reasoning for $b>0$ and integers $m$, $n>1$?
7. Let $f(x)=x^2-4x+1$ and $g(x)=3x-5$. Find $(f+g)(x)$.​
8. A ball's height (in meters) after $t$ seconds is modeled by $H(t)=-t^2+6t+1$. Use completing the square to find the maximum height and when it occurs.
9. In the expression $(x + 4)(x - 2)$, what are the factors?
10. If $m(x)=2x^2-3x+1$, evaluate $m(-1)$.
11. Multiply and simplify the rational expressions (the result will also be a rational expression): $\frac{x^2-9}{x^2-4}\cdot\frac{x+2}{x-3}$
12. Sarah parks for 2.7 hours. If the equation $P(2.7) = c$ represents her total cost, what does the expression $P(2.7) - P(1.3)$ represent?
13. A quantity follows this table: $t$: 0, 1, 2, 3 $y$: 50, 55, 60, 65 From the table, determine if there is constant percent change. If so, what is the percent rate per time unit?
14. A bacteria culture starts with 200 bacteria and increases by 10% each hour. Write a function $P(t)$ for the population after $t$ hours.
15. What are the quotient $q(x)$ and remainder $r(x)$ when dividing $x^3-4x^2+x+6$ by $x-3$? Then write $\frac{x^3-4x^2+x+6}{x-3}=q(x)+\frac{r(x)}{x-3}$ with $\deg(r)<1$.
16. A bacteria population doubles every 3 hours. If the initial population is 500 bacteria, which equation can be used to find the time $t$ (in hours) when the population first exceeds 10,000?
17. In the expression $6x(x - 3)$, what are the factors of $6x(x - 3)$?
18. The population of bacteria in a petri dish is modeled by $P(t) = 250 \cdot 3^{0.5t}$, where $t$ is time in hours. A scientist observes that after 4 hours, the population has grown significantly. What does the value 0.5 in the exponent most directly represent?
19. Factor $f(x)=x^2+6x+8$ to find the zeros and the axis of symmetry.
20. Solve and check for extraneous solutions: $\frac{x}{x-3}=2.$

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